prove the identity 1cos2psi1cos2theta cos2psicos2thetaSolut

prove the identity: 1+cos2psi/1+cos2theta = cos^2psi/cos^2theta

Solution

1+cos2psi/1+cos2theta = cos^2psi/cos^2theta

LHS : 1+cos2psi/1+cos2theta

Use the trigonometrice formula : cos2x = 2cos^2x -1

1+cos2psi/1+cos2theta = ( 1 + 2cos^2psi -1)/( 1 + 2cos^2theta -1)

= 2cos^2psi/2cos^2theta

=  cos^2psi/cos^2theta

RHS